Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.aayq)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 4 and fixed z

For fixed z and a=-17/4, b>=a

For fixed z and a=-17/4, b=11/2

http://functions.wolfram.com/07.23.03.aayq.01

Input Form

Hypergeometric2F1[-(17/4), 11/2, 4, z] == (8 Sqrt[2] (2 (-28288 - 259896 z - 2837640 z^2 + 165874750 z^3 - 793712175 z^4 + 1432135089 z^5 - 1129697877 z^6 + 328582485 z^7) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 2 Sqrt[1 - z] (-28288 - 259896 z - 2837640 z^2 + 165874750 z^3 - 793712175 z^4 + 1432135089 z^5 - 1129697877 z^6 + 328582485 z^7) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(3/4) (28288 + 274040 z + 2979080 z^2 - 76016150 z^3 + 251089275 z^4 - 287900844 z^5 + 109527495 z^6) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (-28288 - 259896 z - 2837640 z^2 + 165874750 z^3 - 793712175 z^4 + 1432135089 z^5 - 1129697877 z^6 + 328582485 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(1/4) (-28288 - 259896 z - 2837640 z^2 + 165874750 z^3 - 793712175 z^4 + 1432135089 z^5 - 1129697877 z^6 + 328582485 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - Sqrt[1 - z] (-28288 - 259896 z - 2837640 z^2 + 165874750 z^3 - 793712175 z^4 + 1432135089 z^5 - 1129697877 z^6 + 328582485 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))/ (353296125 Pi Sqrt[1 + Sqrt[1 - z]] z^3)

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]